Curcumin is a natural bioactive compound with remarkable therapeutic potential; however, its poor aqueous solubility and limited bioavailability have hindered its clinical application. In this study, biodegradable L-aspartic acid-grafted methyl cellulose (MC-g-Asp) nanoparticles were successfully developed as a pH-responsive nanocarrier for the sustained delivery of curcumin. The synthesized nanoparticles were characterized by Fourier transform infrared spectroscopy (FTIR), dynamic light scattering (DLS), zeta potential analysis, thermogravimetric analysis (TGA), and differential scanning calorimetry (DSC), confirming successful grafting, efficient drug encapsulation, favorable colloidal stability, and enhanced thermal stability. In vitro release studies revealed a biphasic release profile consisting of an initial burst release followed by sustained drug release, reaching approximately 89% at pH 5.5 and 68% at pH 7.4 after 72 h. Drug release kinetics were best described by the Korsmeyer–Peppas model, indicating an anomalous transport mechanism governed by both diffusion and polymer relaxation. MTT assay demonstrated excellent biocompatibility of the blank nanocarrier, while curcumin-loaded nanoparticles exhibited significant concentration- and time-dependent cytotoxicity against MCF-7 breast cancer cells, with an IC₅₀ of approximately 92 μg mL⁻¹ after 48 h. These findings demonstrate that MC-g-Asp nanoparticles represent a promising biodegradable platform for pH-responsive and sustained curcumin delivery with potential applications in anticancer therapy.